Question

How is the expected frequency in any given cell of a contingency table determined?

Answer 1

Expected frequencies are calculated for each cell in a contingency table by the formula :

$\dpi{100} \fn_cm E_{ij} =\frac{T_{i}\times T'_{j} }{N}$

• E_ij = expected frequency for the i^th row and j^th column
• T_i = total in the i^th row
• T'_j = total in the j^th column
• N = table grand total

For example

	Y1	Y2	Total
X1	5	10	15=Ti or T1
X2	15	20	35
Total	20	30 = Tj or T2	50 = N

$\dpi{100} \fn_cm E_{12} =\frac{T_{1}\times T'_{2} }{N}$

$\dpi{100} \fn_cm =\frac{15\times 30 }{50} = 9$